Theorem mbf0

Description: The empty function is measurable. (Contributed by Brendan Leahy, 28-Mar-2018)

	Ref	Expression
Assertion	mbf0	⊢ ∅ ∈ MblFn

Proof

Step	Hyp	Ref	Expression
1		0xp	⊢ ( ∅ × { 1 } ) = ∅
2		0mbl	⊢ ∅ ∈ dom vol
3		ax-1cn	⊢ 1 ∈ ℂ
4		mbfconst	⊢ ( ( ∅ ∈ dom vol ∧ 1 ∈ ℂ ) → ( ∅ × { 1 } ) ∈ MblFn )
5	2 3 4	mp2an	⊢ ( ∅ × { 1 } ) ∈ MblFn
6	1 5	eqeltrri	⊢ ∅ ∈ MblFn